Numerals : New Dresses for Old Numbers

Citation preview

1511

Ad5n 1251039

Adler

Numerals, new dresses for old lumbers Stop

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PUBLIC LIBRARY Fort Izyne and Allen County, Indiana

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ALLEN COUNTY PUBLIC LIBRARY

3 1833 00574 0029

Digitized by the Internet Archive in

2011

http://www.archive.org/details/numeralsnewdressOOadle

The "Reason Why" Books

NUMERALS J

New

Dresses for Old

Irving and

Numbers

Ruth Adler

The John Day Company

— New

York

J 5/f 8

2183

3

The "Reason Why" Books by Irving and Ruth Adler AIR INSECTS AND PLANTS IRRIGATION: CHANGING DESERTS INTO GARDENS NUMERALS: NEW DRESSES FOR OLD NUMRERS

NUMRERS OLD AND NEW OCEANS RIVERS

SHADOWS STORMS THE EARTH'S CRUST THE STORY OF A NAIL THINGS THAT SPIN WHY? A ROOK OF REASONS WHY AND HOW? A SECOND ROOK OF REASONS YOUR EARS YOUR EYES

© 1964 by Irving and Ruth Adler must not be reproduced in any form without permission. Published by The John Day Company, Inc., 62 West 45th Street, New York 36, N.Y., and simultaneously in Canada by All rights reserved. This book, or parts thereof,

Longmans Canada Limited, Toronto.

Library of Congress Catalogue Card Number: 64-10448

MANUFACRTRED

IN

THE UNITED STATES OF AMERICA

1251039 Contents Dresses for

Counting If

The

6

Only Eight Fingers

of a System of

Numerals

to

Changing

to a

Way

8

12

Places

Base Ten

Changing

Short

7

10

Digits

More Than Two

A

4

Groups of Ten

in

We Had

The Base

Numbers

Not Ten

20

Changing Numerals

24

Base That

of

16 Is

Addition and Multiplication Tables

28

Multiplying by 10

35

Adding and Multiplying

36

Computers and Base

Word

List

Answers

to Questions

Two Numerals

44 46 46

one five

ten

BB HH

Arabic

Roman

i

I

5

V X

Hi Dresses for

Every number has

one

y,

own name.

its

In the

number of fingers on a hand has the name five. The number of fingers on both your hands has the name ten. English language, the

When we do name

two

Numbers

of each

arithmetic, while

number we

use,

the name. Instead

we

symbol (SIM-buhl)

for the

we

we do

say the

not write

write a special sign or

number.

We write

number one, 5 for the number five, and 10 for the number ten. Written symbols 1 for

the

5 and 10 that stand for numbers are

like 1,

Jk

called numerals (NOOM-er-uhls).

five

The numerals of numerals that

family

is

merals, or 10,

known

1,

5 and 10 belong to a family

we

got from the Arabs. This

as the Arabic

and each member

is

system of nu-

of the family, like 5

called an Arabic numeral.

On some old clock faces, the symbols I, V and X are used in the place of 1, 5 and 10. The symbols I, V and X are called Roman numer-

These numbers

one two ten

twelve

Greek

Babylonian

^BBBH^^B

\s

Egyptian 1

V.'

E

n

K

als

because they belong to a different system

we got from the Romans. many other systems of numerals

Different numerals for

of numerals that

There are

besides the Arabic and the of this

three

hundred twelve

Roman. At the top

page you see some numerals that be-

long to the old systems of the Egyptians, the Greeks, and the Babylonians. At the bottom are numerals that belong to

Arabic

some new systems

-ihqplHr

that look almost like the Arabic system.

A

numeral

wears.

A

like a dress that a

is

system of numerals

is

number

3* IP

like a style of

The numeral 10 is the dress that the number ten wears in the Arabic style. The numeral X is the dress that the same number dress.

wears

in the

Roman

Hebrew

HHhjHri

style.

999011

You can learn more about the old dresses that numbers used to wear by reading the book Numbers Old and New.* In this book you

will learn

that give us *

By

about

new

the same authors.

new

Egyptian s~\

systems of numerals

dresses for the old numbers.

The John Day Company, New York, 1960.

Mayan w w w ~w

base twelve f

nerals

v.,

L. '
4 x

1

=

72

= 4 =

4twelve

76

lO

X

*

x

3

12 1

T 3 twelve

=

120

=

3

=

123

Example: Change 123tweive

Example: Change 20Etweive

to a base ten numeral.

to a base ten numeral.

!

X

12

2

X

12

r*3 X r; 1

one, 12 for twelve,

1

2 3 twelve

Question

29Ttwe ive

13.

x

12

=

2X12X12 =

144

= 24

—»

X

12

=

=

3

r-M1 x

1

=

=

171

2

E twelve

288

11

= 299

Change 37 tWeive, E4 twe Ve, 150 tW eive, and i

to base ten numerals.

Question. 14.

Write

all

the digits for the system of nu-

merals with base eleven. In a base eleven numeral, what

number does the third place from the right belong Change 4T e eV en and 206 e e ven to base ten numerals. i

i

to?

17

To understand ber that the

first

second place

place on the right

is

we must remem-

the ones place.

The

the sevens place, and the third place

is

X

the (seven

a base seven numeral,

seven)s place. Then, using base ten numer-

we can write seven X seven. als,

1 for one,

X

7 for seven, and 7

7 for

Example: Change 52 S even

Example: Change 35 S even

to a base ten numeral.

to a

=

35

2X1=

2

=

37

X

5

7

5 2

X

7

=

1

=6

[-6 X

=

6 seven

Question

to a

>2 x

5

=

26

7

1X7 4X1

55

Change 66,

15.

-5X1=

base ten numeral.

= 49

7

7

21

Example: Change 214 se ven

x

—O I

X

=

7

3 5 seven

base ten numeral. 1

base ten numeral.

*3 X

Example: Change 106 S even to a

is

2

i,

I

4 seven

X

7

=

98

=7 =4 =

109

43 seve n, 312 seve n, and 104,

to base ten numerals.

Question

Write

16.

merals with base

six.

all

the digits for the system of nu-

In a base

six

numeral, what number

does the third place from the right belong to? Change

25 six and 314 six

to base ten numerals.

To understand ber that the

18

first

second place

is

a base

two numeral, we must remem-

place on the right

is

the ones place.

the twos place, and the third place

is

The the

X

X two X two)s place, and the fifth place is the (two X two X two X two)s place. Then, using base ten numerals, we can write 1 for one, 2 for two, 2 X 2 for two X two, 2 X 2 X 2 for two X two X two, and so on. (two

two)s place.

The

fourth place

is

the (two

Example: Change lOOtwo

Example: Change llltwo

to a base ten numeral.

to a base ten numeral.

= 4

1

Ox

2

=

1X2

=2

X

1

=

1X1

=

—

|

c)

O

= 4

Otwo

1

Example: Change 10101 to a

base ten numeral.

-1

X2x2x2x2

=

x

1

1two

Question

X

2

1

=7

base ten numeral.

16

!

X

16

=

16

=

1X8=8

= 4

OX

4

=

1X2=2

=

1

=

21

1X1=1 1

Change 101 two

17.

2

two

=

r

X

Example: Change HOlltwo

two

to a

0x2x2x2 1x2x2 0X2 1

= 4

*1 X 2 X 2

,

110 tW o,

=

1two

11001 tW o,

27

and

10001 two to base ten numerals. Question

18.

Write

all

the digits for the system of nu-

merals with base three. In a base three numeral, what

numbers do the

third

and fourth places from the

belong to? Change 102 numerals.

t

h re e

and 12 12 three

right

to base ten

h

Changing

Base That

to a

Not Ten

Is

In the base eight numeral for a number, only one place is

used

if

the

number

less

is

than

The second place

8.

number is at least as much as 8. The third place is used if the number is at least as much as 8 X 8. The fourth place is used if the number

from the right

is

at least as

is

used

much

the

if

as 8

X

8

X

8,

and

so on.

we Then we

To find the base eight numeral for a number, find out

which places are used

numeral.

in the

first

find the digit for each place.

.......

... Example: Write the base eight numeral for

The first place from the right belongs to 1. 1 is not more than 358, so the first place is used. The second place belongs to 8. 8 is not more than 358, so the second place

is

used.

The third place belongs

to 8

than 358, so the third place

is

X

8

=

64.

64

is

not more

used.

The fourth place belongs to 8 X 8 X 8 = 512. 512 is more than 358, so the fourth place is not used. To find the digit for the third place, find out how many sixty-fours are in 358:

64

64

64

64

64

64

XI

X2

X3

X4

X5

X6

64

128

192

256

320

384

There are 5

sixty-fours, or 320, in 358.

the third place

20

is 5.

To find the digit many eights are in

358

-

320

=

So the

digit for

38.

for the second place, find out

38:

how

There are 4

ond place

8

8

8

8

8

XI

X2

X3

X4

X5

8

16

24

32

40

eights, or 32, in 38.

38

is 4.

To find

-32 =

the digit for the

ones are in

6.

=

Then 358

6

(5

X 1 = X 64) +

So the digit for the

6. first

how many

there are 6 ones in

6, so

(4

place, find out

X

8)

+

Example: Write the base eight numeral Place

(6

for

Place value

X

1)

=

.

277. place used?

Is this

1

yes-

Second

8

yes

64

yes

Third

6.

546 eight

First

512

Fourth

sec-

no

Third Place:

64

64

64

64

64

XI

X2

X3

X4

X5

64

128

192

256

320

8

8

8

XI

X2

X3

8

16

24

277

=

256 21

Second Place: 21

-

16

=

5.

First Place:

277

=

(4

X

64)

+

(2

X

8)

+

(5

X

1)

=

425 eigh

t.

19.

Write the base eight numeral for 201.

Question 20.

Write the base eight numeral for 168.

Question

21

In the base twelve numeral for a number, only one

place

is

used

if

the

number

place from the right big as 12.

The

as big as 12

To find find out

third place

X

and

12,

is

less

if

the

used

is

is

used

if

than 12. The second number is at least as the number is at least

so on.

we Then we

the base twelve numeral for a number,

which places are used

in the numeral.

first

find the digit for each place.

Example: Write the base twelve numeral

Place

for

Place value

Third

Is this

yes

12

yes

144

yes

1728

Fourth

place used?

1

First

Second

466.

no

Third Place:

144

L44

144

144

XI

X2

X3

X4

288

432

576

12

12

12

XI

X2

X3

12

24

36

144

i

466

=

432 34.

Second Place: 34

-

24

=

10.

First Place:

T X 466

22

1

=

= (3X

10.

(T

144)

is

the base twelve digit for ten.

4- (2

X

12)

+

(T

X

1)

=

32T twel ve